Question

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Answer 1

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1.     F(x)= x+2 ,

(f ο g) (x) = 3x- 5,

g(x)?            

(f o g) = f( gx) = 3x-5

               g(x)+2 = 3x-5

               g(x) = 3x-7

 

2.     F(x)= x-1,

(f o g)(x) = X2 + 2x -2 ,

g(x) ?

(f o g) = f (gx) = X2 + 2x -2

               g(x)-1 = X2 + 2x -2

               g(x) =X2 + 2x -1

 

3.     g(x)= x-1,  

(f o g)(x) = 3x - 5 ,

 f(x) ?

(f o g) = f (gx) = 3x-5

               F (x-1) = 3x-5

               F (x) = 3 g^-1 – 5   à g(x) = x-1

                                                        Y = x-1 à x= y+1

                                                                          g^-1 = x+1

                f(x) = 3 (x+1)-5    

                        = 3x+3-5

                        = 3x-2

 

4.     g(x) = x + 3,

(f o g)(x) = X2 + 8x + 10,

F(x) ?

 

(fog)= f(gx) = X2 + 8x + 10

           F(x+3) = X2 + 8x + 10

              F(x) = (g^-1) 2+8(g^-1)+10   à g(x) =x+3

                                                                           Y = x+3 à x=y-3

                                                                                          g^-1 = x-3

 

              f(x) = (x-3)2+8(x-3)+10

                     = x2-6x+9+8x-24+10

                     = x2+2x -5